...seconds, and the space a «3 will be = 9»»; in four seconds, it will be = 16 ss. Hence it is shown that the space described is proportional to the square of the time. 125. Again, when P has moved for one second, let the ring, r (which is movable up and down), be placed...

...change the positions of A and B, but still o B will equal 4.OA. This result is consistent with the rule that the space described is proportional to the square of the time of description (« = } / 1-, or t oo #2). And the rule may be further confirmed by comparing the spaces described...

...s= 4 gtz ; the former indicating that the velocity acquired is proportional to the time; the latter, that the space described is proportional to the square of the time employed. Again, there are the three great Keplerian laws touching the solar system ; — 1°, That...

...£ gtz ; the former indicating that the velocity acquired is proportional to the time; the latter, that the space described is proportional to the square of the time employed. Again, there are the three great Keplerian laws touching the solar system ; — 1°, That...

...seconds, and the space * s, will be = 9 s st ; in four seconds it will be=16 * *j. Hence it is shown that the space described is proportional to the square of the time. 188. Again, when P has moved for one second, let the ring, v (which is movable up and down), be placed...

...the tangent cuts off equal intercepts from the axes. [NB— This requires that tan $ = ± 1.] 1 9. Prove that if a particle move so that the space described...increase of the velocity will be constant. 20. Show that if « oc sin nt, where n is a constant, the rate of iucrease of the velocity is proportional to...

...seconds. (3) Show, by means of a diagram, that when a body moves from rest under a uniform acceleration, the space described is proportional to the square of the time of the motion. (4) A diagram is constructed whose abscissae represent times on a scale of one minute to...

...the tangent cuts off equal intercepts from the axes. [NB— This requires that tan л/л = +1.] 6. Prove that if a particle move so that the space described...time, and the rate of increase of the velocity will Ъе constant. 7. Shew that if a particle moves so that the space described is given by s oc sin ¡it,...

...is uniform, the mean velocity acquired at Then, 8 = £ Xt = V2gt2. Since y2g is constant, it follows that, the space described is proportional to the square of the time. By eliminating t from equations (i) and (2), the relation between v and j can be obtained. From equation...

...during t seconds with the mean velocity —. Then S=1T xt—^gi'- (2) Since \g is constant, it follows that the space described is proportional to the square of the time. By eliminating / from equations (i) and (2), the relation between v and .? can be obtained. From equation...